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Grade 12th passVectors

a,b,c, and d are the position vectors of four cop

a,b,c, and d are the position vectors of four coplanar points such that (a-d).(b-c)=(b-d).(c-a)=0  .  Show that the point d represents the orthocentre of the triangle with a,b and c as its vertices
Profile image of Saurav kumar Sagar
8 Years agoGrade 12th pass
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1 Answer

Profile image of Arun

Arun

8 Years ago
Dear student
 
First equation means that
AD\perp BC
Second equation means
BD \perp CA
Then D is the intersection of altitudes through A and B. Hence D is orthocentre.